Question about Lucena position in Practice

I know the usual Lucena position, but I can't understand this "Alternative" way in Practice.
lichess.org/practice/rook-endgames/basic-rook-endgames/pqUSUw8Y/hg6wz0gX

The explanation says:
to maneuver the rook to the g8-square and budge Black's rook from that file, then simply marching forward with the king until there are no checks left.

However, after
1. Rh1 Rf2 2. Rh8 Ra2 3. Rg8 Ke6 4. Kg7 Rg2+
I don't know what to do.
moving back the king doesn't work because
5. Kh6 Rh2+ 6. Kg5 Kxf7
and the pawn is lost.
The engine says 4. Rg6, but it doesn't fit the explanation.

I wish that the explanation is written in more detail.

@Lamiales said in #1:
> I know the usual Lucena position, but I can't understand this "Alternative" way in Practice.
> lichess.org/practice/rook-endgames/basic-rook-endgames/pqUSUw8Y/hg6wz0gX
>
> The explanation says:
> to maneuver the rook to the g8-square and budge Black's rook from that file, then simply marching forward with the king until there are no checks left.

That is a bit too simplified, I would say.

> However, after
> 1. Rh1 Rf2 2. Rh8 Ra2 3. Rg8 Ke6 4. Kg7 Rg2+
> I don't know what to do.
> moving back the king doesn't work because
> 5. Kh6 Rh2+ 6. Kg5 Kxf7
> and the pawn is lost.
> The engine says 4. Rg6, but it doesn't fit the explanation.
>
> I wish that the explanation is written in more detail.

After reaching the g8-square and conquering the g-file, the white rook has to retreat on the file, e.g. 4. Rg6+, 4. Rg3 or 4. Rg1. Then the king can go to g7 or g8 without getting checked from behind, and the pawn promotes.

If Black does not play 4... Ke6, then leaving the rook on g8 and zigzagging the king back on the g- and h-files works, but after 4... Ke6 it does not, as you have noticed.

@zwenna said in #2:
> That is a bit too simplified, I would say.
>
>
>
> After reaching the g8-square and conquering the g-file, the white rook has to retreat on the file, e.g. 4. Rg6+, 4. Rg3 or 4. Rg1. Then the king can go to g7 or g8 without getting checked from behind, and the pawn promotes.
>
> If Black does not play 4... Ke6, then leaving the rook on g8 and zigzagging the king back on the g- and h-files works, but after 4... Ke6 it does not, as you have noticed.

Thank you! Now I understand it.
I hope Lichess will add more explanation.

In the Lucena position, the key concept is to isolate the pawn, so that it does not get attacked twice.

As the pawn advances towards promotion, ensure that the opposing king and rook cannot simultaneously threaten the pawn.